Apparatus and method for rendering adaptive mesh refinement (amr) data

ABSTRACT

An apparatus and method are described for rendering adaptive mesh refinement data. For example, one embodiment of a graphics processing apparatus comprises: a tree data structure generator to transform adaptive mesh refinement (AMR) data into a multi-octree or kd-tree data structure, respectively; an interpolator to implement an interpolation scheme based on the multi-octree or kd-tree data structure to generate interpolated results, the interpolation scheme using repeated linear interpolation; and a ray tracing-based renderer to use the interpolated results to render image frames using ray tracing techniques.

BACKGROUND Field of the Invention

This invention relates generally to the field of computer processors.More particularly, the invention relates to an apparatus and method forrending adaptive mesh refinement (AMR) data.

Description of the Related Art

Adaptive Mesh Refinement (AMR) schemes are increasingly used by varioussimulation codes to better focus memory and compute resources to areasthat matter more than others. This makes it imperative to render themefficiently, but it is not trivial to do so.

There are a variety of different AMR schemes, differing in whether theyhave structured or unstructured grids; cuboid, hexahedral, ortetrahedral cells; use cell-centered or vertex-centered data points,etc. One of the most widely used such schemes is the Berger-Colellascheme as used in, for example, the Lawrence Berkeley Lab's “Chombo”simulation code.

BRIEF DESCRIPTION OF THE DRAWINGS

A better understanding of the present invention can be obtained from thefollowing detailed description in conjunction with the followingdrawings, in which:

FIG. 1 is a block diagram of an embodiment of a computer system with aprocessor having one or more processor cores and graphics processors;

FIG. 2 is a block diagram of one embodiment of a processor having one ormore processor cores, an integrated memory controller, and an integratedgraphics processor;

FIG. 3 is a block diagram of one embodiment of a graphics processorwhich may be a discreet graphics processing unit, or may be graphicsprocessor integrated with a plurality of processing cores;

FIG. 4 is a block diagram of an embodiment of a graphics-processingengine for a graphics processor;

FIG. 5 is a block diagram of another embodiment of a graphics processor;

FIG. 6 is a block diagram of thread execution logic including an arrayof processing elements;

FIG. 7 illustrates a graphics processor execution unit instructionformat according to an embodiment;

FIG. 8 is a block diagram of another embodiment of a graphics processorwhich includes a graphics pipeline, a media pipeline, a display engine,thread execution logic, and a render output pipeline;

FIG. 9A is a block diagram illustrating a graphics processor commandformat according to an embodiment;

FIG. 9B is a block diagram illustrating a graphics processor commandsequence according to an embodiment;

FIG. 10 illustrates exemplary graphics software architecture for a dataprocessing system according to an embodiment;

FIG. 11 illustrates an exemplary IP core development system that may beused to manufacture an integrated circuit to perform operationsaccording to an embodiment;

FIG. 12 illustrates an exemplary system on a chip integrated circuitthat may be fabricated using one or more IP cores, according to anembodiment;

FIG. 13 illustrates an exemplary graphics processor of a system on achip integrated circuit that may be fabricated using one or more IPcores;

FIG. 14 illustrates an additional exemplary graphics processor of asystem on a chip integrated circuit that may be fabricated using one ormore IP cores

FIG. 15 illustrates exemplary adaptive mesh refinement (AMR) techniques;

FIG. 16A illustrates an alignment of different AMR cells acrossdifferent levels;

FIG. 16B illustrates a smooth continuous interpolation is through“stitching” across boundaries;

FIGS. 17A-B illustrate exemplary graphics processing engines inaccordance with embodiments of the invention;

FIGS. 18A-B illustrate exemplary geometry for a cell, one of itsoctants, the vertices thereof, and neighbor cells.

DETAILED DESCRIPTION

In the following description, for the purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of the embodiments of the invention described below. Itwill be apparent, however, to one skilled in the art that theembodiments of the invention may be practiced without some of thesespecific details. In other instances, well-known structures and devicesare shown in block diagram form to avoid obscuring the underlyingprinciples of the embodiments of the invention.

Exemplary Graphics Processor Architectures and Data Types

System Overview

FIG. 1 is a block diagram of a processing system 100, according to anembodiment. In various embodiments the system 100 includes one or moreprocessors 102 and one or more graphics processors 108, and may be asingle processor desktop system, a multiprocessor workstation system, ora server system having a large number of processors 102 or processorcores 107. In one embodiment, the system 100 is a processing platformincorporated within a system-on-a-chip (SoC) integrated circuit for usein mobile, handheld, or embedded devices.

An embodiment of system 100 can include, or be incorporated within aserver-based gaming platform, a game console, including a game and mediaconsole, a mobile gaming console, a handheld game console, or an onlinegame console. In some embodiments system 100 is a mobile phone, smartphone, tablet computing device or mobile Internet device. Dataprocessing system 100 can also include, couple with, or be integratedwithin a wearable device, such as a smart watch wearable device, smarteyewear device, augmented reality device, or virtual reality device. Insome embodiments, data processing system 100 is a television or set topbox device having one or more processors 102 and a graphical interfacegenerated by one or more graphics processors 108.

In some embodiments, the one or more processors 102 each include one ormore processor cores 107 to process instructions which, when executed,perform operations for system and user software. In some embodiments,each of the one or more processor cores 107 is configured to process aspecific instruction set 109. In some embodiments, instruction set 109may facilitate Complex Instruction Set Computing (CISC), ReducedInstruction Set Computing (RISC), or computing via a Very LongInstruction Word (VLIW). Multiple processor cores 107 may each process adifferent instruction set 109, which may include instructions tofacilitate the emulation of other instruction sets. Processor core 107may also include other processing devices, such a Digital SignalProcessor (DSP).

In some embodiments, the processor 102 includes cache memory 104.Depending on the architecture, the processor 102 can have a singleinternal cache or multiple levels of internal cache. In someembodiments, the cache memory is shared among various components of theprocessor 102. In some embodiments, the processor 102 also uses anexternal cache (e.g., a Level-3 (L3) cache or Last Level Cache (LLC))(not shown), which may be shared among processor cores 107 using knowncache coherency techniques. A register file 106 is additionally includedin processor 102 which may include different types of registers forstoring different types of data (e.g., integer registers, floating pointregisters, status registers, and an instruction pointer register). Someregisters may be general-purpose registers, while other registers may bespecific to the design of the processor 102.

In some embodiments, processor 102 is coupled with a processor bus 110to transmit communication signals such as address, data, or controlsignals between processor 102 and other components in system 100. In oneembodiment the system 100 uses an exemplary ‘hub’ system architecture,including a memory controller hub 116 and an Input Output (I/O)controller hub 130. A memory controller hub 116 facilitatescommunication between a memory device and other components of system100, while an I/O Controller Hub (ICH) 130 provides connections to I/Odevices via a local I/O bus. In one embodiment, the logic of the memorycontroller hub 116 is integrated within the processor.

Memory device 120 can be a dynamic random access memory (DRAM) device, astatic random access memory (SRAM) device, flash memory device,phase-change memory device, or some other memory device having suitableperformance to serve as process memory. In one embodiment the memorydevice 120 can operate as system memory for the system 100, to storedata 122 and instructions 121 for use when the one or more processors102 executes an application or process. Memory controller hub 116 alsocouples with an optional external graphics processor 112, which maycommunicate with the one or more graphics processors 108 in processors102 to perform graphics and media operations.

In some embodiments, ICH 130 enables peripherals to connect to memorydevice 120 and processor 102 via a high-speed I/O bus. The I/Operipherals include, but are not limited to, an audio controller 146, afirmware interface 128, a wireless transceiver 126 (e.g., Wi-Fi,Bluetooth), a data storage device 124 (e.g., hard disk drive, flashmemory, etc.), and a legacy I/O controller 140 for coupling legacy(e.g., Personal System 2 (PS/2)) devices to the system. One or moreUniversal Serial Bus (USB) controllers 142 connect input devices, suchas keyboard and mouse 144 combinations. A network controller 134 mayalso couple with ICH 130. In some embodiments, a high-performancenetwork controller (not shown) couples with processor bus 110. It willbe appreciated that the system 100 shown is exemplary and not limiting,as other types of data processing systems that are differentlyconfigured may also be used. For example, the I/O controller hub 130 maybe integrated within the one or more processor 102, or the memorycontroller hub 116 and I/O controller hub 130 may be integrated into adiscreet external graphics processor, such as the external graphicsprocessor 112.

FIG. 2 is a block diagram of an embodiment of a processor 200 having oneor more processor cores 202A-202N, an integrated memory controller 214,and an integrated graphics processor 208. Those elements of FIG. 2having the same reference numbers (or names) as the elements of anyother figure herein can operate or function in any manner similar tothat described elsewhere herein, but are not limited to such. Processor200 can include additional cores up to and including additional core202N represented by the dashed lined boxes. Each of processor cores202A-202N includes one or more internal cache units 204A-204N. In someembodiments each processor core also has access to one or more sharedcached units 206.

The internal cache units 204A-204N and shared cache units 206 representa cache memory hierarchy within the processor 200. The cache memoryhierarchy may include at least one level of instruction and data cachewithin each processor core and one or more levels of shared mid-levelcache, such as a Level 2 (L2), Level 3 (L3), Level 4 (L4), or otherlevels of cache, where the highest level of cache before external memoryis classified as the LLC. In some embodiments, cache coherency logicmaintains coherency between the various cache units 206 and 204A-204N.

In some embodiments, processor 200 may also include a set of one or morebus controller units 216 and a system agent core 210. The one or morebus controller units 216 manage a set of peripheral buses, such as oneor more Peripheral Component Interconnect buses (e.g., PCI, PCIExpress). System agent core 210 provides management functionality forthe various processor components. In some embodiments, system agent core210 includes one or more integrated memory controllers 214 to manageaccess to various external memory devices (not shown).

In some embodiments, one or more of the processor cores 202A-202Ninclude support for simultaneous multi-threading. In such embodiment,the system agent core 210 includes components for coordinating andoperating cores 202A-202N during multi-threaded processing. System agentcore 210 may additionally include a power control unit (PCU), whichincludes logic and components to regulate the power state of processorcores 202A-202N and graphics processor 208.

In some embodiments, processor 200 additionally includes graphicsprocessor 208 to execute graphics processing operations. In someembodiments, the graphics processor 208 couples with the set of sharedcache units 206, and the system agent core 210, including the one ormore integrated memory controllers 214. In some embodiments, a displaycontroller 211 is coupled with the graphics processor 208 to drivegraphics processor output to one or more coupled displays. In someembodiments, display controller 211 may be a separate module coupledwith the graphics processor via at least one interconnect, or may beintegrated within the graphics processor 208 or system agent core 210.

In some embodiments, a ring based interconnect unit 212 is used tocouple the internal components of the processor 200. However, analternative interconnect unit may be used, such as a point-to-pointinterconnect, a switched interconnect, or other techniques, includingtechniques well known in the art. In some embodiments, graphicsprocessor 208 couples with the ring interconnect 212 via an I/O link213.

The exemplary I/O link 213 represents at least one of multiple varietiesof I/O interconnects, including an on package I/O interconnect whichfacilitates communication between various processor components and ahigh-performance embedded memory module 218, such as an eDRAM module. Insome embodiments, each of the processor cores 202A-202N and graphicsprocessor 208 use embedded memory modules 218 as a shared Last LevelCache.

In some embodiments, processor cores 202A-202N are homogenous coresexecuting the same instruction set architecture. In another embodiment,processor cores 202A-202N are heterogeneous in terms of instruction setarchitecture (ISA), where one or more of processor cores 202A-202Nexecute a first instruction set, while at least one of the other coresexecutes a subset of the first instruction set or a differentinstruction set. In one embodiment processor cores 202A-202N areheterogeneous in terms of microarchitecture, where one or more coreshaving a relatively higher power consumption couple with one or morepower cores having a lower power consumption. Additionally, processor200 can be implemented on one or more chips or as an SoC integratedcircuit having the illustrated components, in addition to othercomponents.

FIG. 3 is a block diagram of a graphics processor 300, which may be adiscrete graphics processing unit, or may be a graphics processorintegrated with a plurality of processing cores. In some embodiments,the graphics processor communicates via a memory mapped I/O interface toregisters on the graphics processor and with commands placed into theprocessor memory. In some embodiments, graphics processor 300 includes amemory interface 314 to access memory. Memory interface 314 can be aninterface to local memory, one or more internal caches, one or moreshared external caches, and/or to system memory.

In some embodiments, graphics processor 300 also includes a displaycontroller 302 to drive display output data to a display device 320.Display controller 302 includes hardware for one or more overlay planesfor the display and composition of multiple layers of video or userinterface elements. In some embodiments, graphics processor 300 includesa video codec engine 306 to encode, decode, or transcode media to, from,or between one or more media encoding formats, including, but notlimited to Moving Picture Experts Group (MPEG) formats such as MPEG-2,Advanced Video Coding (AVC) formats such as H.264/MPEG-4 AVC, as well asthe Society of Motion Picture & Television Engineers (SMPTE) 421M/VC-1,and Joint Photographic Experts Group (JPEG) formats such as JPEG, andMotion JPEG (MJPEG) formats.

In some embodiments, graphics processor 300 includes a block imagetransfer (BLIT) engine 304 to perform two-dimensional (2D) rasterizeroperations including, for example, bit-boundary block transfers.However, in one embodiment, 2D graphics operations are performed usingone or more components of graphics processing engine (GPE) 310. In someembodiments, GPE 310 is a compute engine for performing graphicsoperations, including three-dimensional (3D) graphics operations andmedia operations.

In some embodiments, GPE 310 includes a 3D pipeline 312 for performing3D operations, such as rendering three-dimensional images and scenesusing processing functions that act upon 3D primitive shapes (e.g.,rectangle, triangle, etc.). The 3D pipeline 312 includes programmableand fixed function elements that perform various tasks within theelement and/or spawn execution threads to a 3D/Media sub-system 315.While 3D pipeline 312 can be used to perform media operations, anembodiment of GPE 310 also includes a media pipeline 316 that isspecifically used to perform media operations, such as videopost-processing and image enhancement.

In some embodiments, media pipeline 316 includes fixed function orprogrammable logic units to perform one or more specialized mediaoperations, such as video decode acceleration, video de-interlacing, andvideo encode acceleration in place of, or on behalf of video codecengine 306. In some embodiments, media pipeline 316 additionallyincludes a thread spawning unit to spawn threads for execution on3D/Media sub-system 315. The spawned threads perform computations forthe media operations on one or more graphics execution units included in3D/Media sub-system 315.

In some embodiments, 3D/Media subsystem 315 includes logic for executingthreads spawned by 3D pipeline 312 and media pipeline 316. In oneembodiment, the pipelines send thread execution requests to 3D/Mediasubsystem 315, which includes thread dispatch logic for arbitrating anddispatching the various requests to available thread executionresources. The execution resources include an array of graphicsexecution units to process the 3D and media threads. In someembodiments, 3D/Media subsystem 315 includes one or more internal cachesfor thread instructions and data. In some embodiments, the subsystemalso includes shared memory, including registers and addressable memory,to share data between threads and to store output data.

Graphics Processing Engine

FIG. 4 is a block diagram of a graphics processing engine 410 of agraphics processor in accordance with some embodiments. In oneembodiment, the graphics processing engine (GPE) 410 is a version of theGPE 310 shown in FIG. 3. Elements of FIG. 4 having the same referencenumbers (or names) as the elements of any other figure herein canoperate or function in any manner similar to that described elsewhereherein, but are not limited to such. For example, the 3D pipeline 312and media pipeline 316 of FIG. 3 are illustrated. The media pipeline 316is optional in some embodiments of the GPE 410 and may not be explicitlyincluded within the GPE 410. For example and in at least one embodiment,a separate media and/or image processor is coupled to the GPE 410.

In some embodiments, GPE 410 couples with or includes a command streamer403, which provides a command stream to the 3D pipeline 312 and/or mediapipelines 316. In some embodiments, command streamer 403 is coupled withmemory, which can be system memory, or one or more of internal cachememory and shared cache memory. In some embodiments, command streamer403 receives commands from the memory and sends the commands to 3Dpipeline 312 and/or media pipeline 316. The commands are directivesfetched from a ring buffer, which stores commands for the 3D pipeline312 and media pipeline 316. In one embodiment, the ring buffer canadditionally include batch command buffers storing batches of multiplecommands. The commands for the 3D pipeline 312 can also includereferences to data stored in memory, such as but not limited to vertexand geometry data for the 3D pipeline 312 and/or image data and memoryobjects for the media pipeline 316. The 3D pipeline 312 and mediapipeline 316 process the commands and data by performing operations vialogic within the respective pipelines or by dispatching one or moreexecution threads to a graphics core array 414.

In various embodiments the 3D pipeline 312 can execute one or moreshader programs, such as vertex shaders, geometry shaders, pixelshaders, fragment shaders, compute shaders, or other shader programs, byprocessing the instructions and dispatching execution threads to thegraphics core array 414. The graphics core array 414 provides a unifiedblock of execution resources. Multi-purpose execution logic (e.g.,execution units) within the graphic core array 414 includes support forvarious 3D API shader languages and can execute multiple simultaneousexecution threads associated with multiple shaders.

In some embodiments the graphics core array 414 also includes executionlogic to perform media functions, such as video and/or image processing.In one embodiment, the execution units additionally includegeneral-purpose logic that is programmable to perform parallel generalpurpose computational operations, in addition to graphics processingoperations. The general purpose logic can perform processing operationsin parallel or in conjunction with general purpose logic within theprocessor core(s) 107 of FIG. 1 or core 202A-202N as in FIG. 2.

Output data generated by threads executing on the graphics core array414 can output data to memory in a unified return buffer (URB) 418. TheURB 418 can store data for multiple threads. In some embodiments the URB418 may be used to send data between different threads executing on thegraphics core array 414. In some embodiments the URB 418 mayadditionally be used for synchronization between threads on the graphicscore array and fixed function logic within the shared function logic420.

In some embodiments, graphics core array 414 is scalable, such that thearray includes a variable number of graphics cores, each having avariable number of execution units based on the target power andperformance level of GPE 410. In one embodiment the execution resourcesare dynamically scalable, such that execution resources may be enabledor disabled as needed.

The graphics core array 414 couples with shared function logic 420 thatincludes multiple resources that are shared between the graphics coresin the graphics core array. The shared functions within the sharedfunction logic 420 are hardware logic units that provide specializedsupplemental functionality to the graphics core array 414. In variousembodiments, shared function logic 420 includes but is not limited tosampler 421, math 422, and inter-thread communication (ITC) 423 logic.Additionally, some embodiments implement one or more cache(s) 425 withinthe shared function logic 420. A shared function is implemented wherethe demand for a given specialized function is insufficient forinclusion within the graphics core array 414. Instead a singleinstantiation of that specialized function is implemented as astand-alone entity in the shared function logic 420 and shared among theexecution resources within the graphics core array 414. The precise setof functions that are shared between the graphics core array 414 andincluded within the graphics core array 414 varies between embodiments.

FIG. 5 is a block diagram of another embodiment of a graphics processor500. Elements of FIG. 5 having the same reference numbers (or names) asthe elements of any other figure herein can operate or function in anymanner similar to that described elsewhere herein, but are not limitedto such.

In some embodiments, graphics processor 500 includes a ring interconnect502, a pipeline front-end 504, a media engine 537, and graphics cores580A-580N. In some embodiments, ring interconnect 502 couples thegraphics processor to other processing units, including other graphicsprocessors or one or more general-purpose processor cores. In someembodiments, the graphics processor is one of many processors integratedwithin a multi-core processing system.

In some embodiments, graphics processor 500 receives batches of commandsvia ring interconnect 502. The incoming commands are interpreted by acommand streamer 503 in the pipeline front-end 504. In some embodiments,graphics processor 500 includes scalable execution logic to perform 3Dgeometry processing and media processing via the graphics core(s)580A-580N. For 3D geometry processing commands, command streamer 503supplies commands to geometry pipeline 536. For at least some mediaprocessing commands, command streamer 503 supplies the commands to avideo front end 534, which couples with a media engine 537. In someembodiments, media engine 537 includes a Video Quality Engine (VQE) 530for video and image post-processing and a multi-format encode/decode(MFX) 533 engine to provide hardware-accelerated media data encode anddecode. In some embodiments, geometry pipeline 536 and media engine 537each generate execution threads for the thread execution resourcesprovided by at least one graphics core 580A.

In some embodiments, graphics processor 500 includes scalable threadexecution resources featuring modular cores 580A-580N (sometimesreferred to as core slices), each having multiple sub-cores 550A-550N,560A-560N (sometimes referred to as core sub-slices). In someembodiments, graphics processor 500 can have any number of graphicscores 580A through 580N. In some embodiments, graphics processor 500includes a graphics core 580A having at least a first sub-core 550A anda second sub-core 560A. In other embodiments, the graphics processor isa low power processor with a single sub-core (e.g., 550A). In someembodiments, graphics processor 500 includes multiple graphics cores580A-580N, each including a set of first sub-cores 550A-550N and a setof second sub-cores 560A-560N. Each sub-core in the set of firstsub-cores 550A-550N includes at least a first set of execution units552A-552N and media/texture samplers 554A-554N. Each sub-core in the setof second sub-cores 560A-560N includes at least a second set ofexecution units 562A-562N and samplers 564A-564N. In some embodiments,each sub-core 550A-550N, 560A-560N shares a set of shared resources570A-570N. In some embodiments, the shared resources include sharedcache memory and pixel operation logic. Other shared resources may alsobe included in the various embodiments of the graphics processor.

Execution Units

FIG. 6 illustrates thread execution logic 600 including an array ofprocessing elements employed in some embodiments of a GPE. Elements ofFIG. 6 having the same reference numbers (or names) as the elements ofany other figure herein can operate or function in any manner similar tothat described elsewhere herein, but are not limited to such.

In some embodiments, thread execution logic 600 includes a shaderprocessor 602, a thread dispatcher 604, instruction cache 606, ascalable execution unit array including a plurality of execution units608A-608N, a sampler 610, a data cache 612, and a data port 614. In oneembodiment the scalable execution unit array can dynamically scale byenabling or disabling one or more execution units (e.g., any ofexecution unit 608A, 608B, 608C, 608D, through 608N-1 and 608N) based onthe computational requirements of a workload. In one embodiment theincluded components are interconnected via an interconnect fabric thatlinks to each of the components. In some embodiments, thread executionlogic 600 includes one or more connections to memory, such as systemmemory or cache memory, through one or more of instruction cache 606,data port 614, sampler 610, and execution units 608A-608N. In someembodiments, each execution unit (e.g. 608A) is a stand-aloneprogrammable general purpose computational unit that is capable ofexecuting multiple simultaneous hardware threads while processingmultiple data elements in parallel for each thread. In variousembodiments, the array of execution units 608A-608N is scalable toinclude any number individual execution units.

In some embodiments, the execution units 608A-608N are primarily used toexecute shader programs. A shader processor 602 can process the variousshader programs and dispatch execution threads associated with theshader programs via a thread dispatcher 604. In one embodiment thethread dispatcher includes logic to arbitrate thread initiation requestsfrom the graphics and media pipelines and instantiate the requestedthreads on one or more execution unit in the execution units 608A-608N.For example, the geometry pipeline (e.g., 536 of FIG. 5) can dispatchvertex, tessellation, or geometry shaders to the thread execution logic600 (FIG. 6) for processing. In some embodiments, thread dispatcher 604can also process runtime thread spawning requests from the executingshader programs.

In some embodiments, the execution units 608A-608N support aninstruction set that includes native support for many standard 3Dgraphics shader instructions, such that shader programs from graphicslibraries (e.g., Direct 3D and OpenGL) are executed with a minimaltranslation. The execution units support vertex and geometry processing(e.g., vertex programs, geometry programs, vertex shaders), pixelprocessing (e.g., pixel shaders, fragment shaders) and general-purposeprocessing (e.g., compute and media shaders). Each of the executionunits 608A-608N is capable of multi-issue single instruction multipledata (SIMD) execution and multi-threaded operation enables an efficientexecution environment in the face of higher latency memory accesses.Each hardware thread within each execution unit has a dedicatedhigh-bandwidth register file and associated independent thread-state.Execution is multi-issue per clock to pipelines capable of integer,single and double precision floating point operations, SIMD branchcapability, logical operations, transcendental operations, and othermiscellaneous operations. While waiting for data from memory or one ofthe shared functions, dependency logic within the execution units608A-608N causes a waiting thread to sleep until the requested data hasbeen returned. While the waiting thread is sleeping, hardware resourcesmay be devoted to processing other threads. For example, during a delayassociated with a vertex shader operation, an execution unit can performoperations for a pixel shader, fragment shader, or another type ofshader program, including a different vertex shader.

Each execution unit in execution units 608A-608N operates on arrays ofdata elements. The number of data elements is the “execution size,” orthe number of channels for the instruction. An execution channel is alogical unit of execution for data element access, masking, and flowcontrol within instructions. The number of channels may be independentof the number of physical Arithmetic Logic Units (ALUs) or FloatingPoint Units (FPUs) for a particular graphics processor. In someembodiments, execution units 608A-608N support integer andfloating-point data types.

The execution unit instruction set includes SIMD instructions. Thevarious data elements can be stored as a packed data type in a registerand the execution unit will process the various elements based on thedata size of the elements. For example, when operating on a 256-bit widevector, the 256 bits of the vector are stored in a register and theexecution unit operates on the vector as four separate 64-bit packeddata elements (Quad-Word (QW) size data elements), eight separate 32-bitpacked data elements (Double Word (DW) size data elements), sixteenseparate 16-bit packed data elements (Word (W) size data elements), orthirty-two separate 8-bit data elements (byte (B) size data elements).However, different vector widths and register sizes are possible.

One or more internal instruction caches (e.g., 606) are included in thethread execution logic 600 to cache thread instructions for theexecution units. In some embodiments, one or more data caches (e.g.,612) are included to cache thread data during thread execution. In someembodiments, a sampler 610 is included to provide texture sampling for3D operations and media sampling for media operations. In someembodiments, sampler 610 includes specialized texture or media samplingfunctionality to process texture or media data during the samplingprocess before providing the sampled data to an execution unit.

During execution, the graphics and media pipelines send threadinitiation requests to thread execution logic 600 via thread spawningand dispatch logic. Once a group of geometric objects has been processedand rasterized into pixel data, pixel processor logic (e.g., pixelshader logic, fragment shader logic, etc.) within the shader processor602 is invoked to further compute output information and cause resultsto be written to output surfaces (e.g., color buffers, depth buffers,stencil buffers, etc.). In some embodiments, a pixel shader or fragmentshader calculates the values of the various vertex attributes that areto be interpolated across the rasterized object. In some embodiments,pixel processor logic within the shader processor 602 then executes anapplication programming interface (API)-supplied pixel or fragmentshader program. To execute the shader program, the shader processor 602dispatches threads to an execution unit (e.g., 608A) via threaddispatcher 604. In some embodiments, pixel shader 602 uses texturesampling logic in the sampler 610 to access texture data in texture mapsstored in memory. Arithmetic operations on the texture data and theinput geometry data compute pixel color data for each geometricfragment, or discards one or more pixels from further processing.

In some embodiments, the data port 614 provides a memory accessmechanism for the thread execution logic 600 output processed data tomemory for processing on a graphics processor output pipeline. In someembodiments, the data port 614 includes or couples to one or more cachememories (e.g., data cache 612) to cache data for memory access via thedata port.

FIG. 7 is a block diagram illustrating a graphics processor instructionformats 700 according to some embodiments. In one or more embodiment,the graphics processor execution units support an instruction set havinginstructions in multiple formats. The solid lined boxes illustrate thecomponents that are generally included in an execution unit instruction,while the dashed lines include components that are optional or that areonly included in a sub-set of the instructions. In some embodiments,instruction format 700 described and illustrated are macro-instructions,in that they are instructions supplied to the execution unit, as opposedto micro-operations resulting from instruction decode once theinstruction is processed.

In some embodiments, the graphics processor execution units nativelysupport instructions in a 128-bit instruction format 710. A 64-bitcompacted instruction format 730 is available for some instructionsbased on the selected instruction, instruction options, and number ofoperands. The native 128-bit instruction format 710 provides access toall instruction options, while some options and operations arerestricted in the 64-bit instruction format 730. The native instructionsavailable in the 64-bit instruction format 730 vary by embodiment. Insome embodiments, the instruction is compacted in part using a set ofindex values in an index field 713. The execution unit hardwarereferences a set of compaction tables based on the index values and usesthe compaction table outputs to reconstruct a native instruction in the128-bit instruction format 710.

For each format, instruction opcode 712 defines the operation that theexecution unit is to perform. The execution units execute eachinstruction in parallel across the multiple data elements of eachoperand. For example, in response to an add instruction the executionunit performs a simultaneous add operation across each color channelrepresenting a texture element or picture element. By default, theexecution unit performs each instruction across all data channels of theoperands. In some embodiments, instruction control field 714 enablescontrol over certain execution options, such as channels selection(e.g., predication) and data channel order (e.g., swizzle). Forinstructions in the 128-bit instruction format 710 an exec-size field716 limits the number of data channels that will be executed inparallel. In some embodiments, exec-size field 716 is not available foruse in the 64-bit compact instruction format 730.

Some execution unit instructions have up to three operands including twosource operands, src0 720, src1 722, and one destination 718. In someembodiments, the execution units support dual destination instructions,where one of the destinations is implied. Data manipulation instructionscan have a third source operand (e.g., SRC2 724), where the instructionopcode 712 determines the number of source operands. An instruction'slast source operand can be an immediate (e.g., hard-coded) value passedwith the instruction.

In some embodiments, the 128-bit instruction format 710 includes anaccess/address mode field 726 specifying, for example, whether directregister addressing mode or indirect register addressing mode is used.When direct register addressing mode is used, the register address ofone or more operands is directly provided by bits in the instruction.

In some embodiments, the 128-bit instruction format 710 includes anaccess/address mode field 726, which specifies an address mode and/or anaccess mode for the instruction. In one embodiment the access mode isused to define a data access alignment for the instruction. Someembodiments support access modes including a 16-byte aligned access modeand a 1-byte aligned access mode, where the byte alignment of the accessmode determines the access alignment of the instruction operands. Forexample, when in a first mode, the instruction may use byte-alignedaddressing for source and destination operands and when in a secondmode, the instruction may use 16-byte-aligned addressing for all sourceand destination operands.

In one embodiment, the address mode portion of the access/address modefield 726 determines whether the instruction is to use direct orindirect addressing. When direct register addressing mode is used bitsin the instruction directly provide the register address of one or moreoperands. When indirect register addressing mode is used, the registeraddress of one or more operands may be computed based on an addressregister value and an address immediate field in the instruction.

In some embodiments instructions are grouped based on opcode 712bit-fields to simplify Opcode decode 740. For an 8-bit opcode, bits 4,5, and 6 allow the execution unit to determine the type of opcode. Theprecise opcode grouping shown is merely an example. In some embodiments,a move and logic opcode group 742 includes data movement and logicinstructions (e.g., move (mov), compare (cmp)). In some embodiments,move and logic group 742 shares the five most significant bits (MSB),where move (mov) instructions are in the form of 0000xxxxb and logicinstructions are in the form of 0001xxxxb. A flow control instructiongroup 744 (e.g., call, jump (jmp)) includes instructions in the form of0010xxxxb (e.g., 0x20). A miscellaneous instruction group 746 includes amix of instructions, including synchronization instructions (e.g., wait,send) in the form of 0011xxxxb (e.g., 0x30). A parallel math instructiongroup 748 includes component-wise arithmetic instructions (e.g., add,multiply (mul)) in the form of 0100xxxxb (e.g., 0x40). The parallel mathgroup 748 performs the arithmetic operations in parallel across datachannels. The vector math group 750 includes arithmetic instructions(e.g., dp4) in the form of 0101xxxxb (e.g., 0x50). The vector math groupperforms arithmetic such as dot product calculations on vector operands.

Graphics Pipeline

FIG. 8 is a block diagram of another embodiment of a graphics processor800. Elements of FIG. 8 having the same reference numbers (or names) asthe elements of any other figure herein can operate or function in anymanner similar to that described elsewhere herein, but are not limitedto such.

In some embodiments, graphics processor 800 includes a graphics pipeline820, a media pipeline 830, a display engine 840, thread execution logic850, and a render output pipeline 870. In some embodiments, graphicsprocessor 800 is a graphics processor within a multi-core processingsystem that includes one or more general purpose processing cores. Thegraphics processor is controlled by register writes to one or morecontrol registers (not shown) or via commands issued to graphicsprocessor 800 via a ring interconnect 802. In some embodiments, ringinterconnect 802 couples graphics processor 800 to other processingcomponents, such as other graphics processors or general-purposeprocessors. Commands from ring interconnect 802 are interpreted by acommand streamer 803, which supplies instructions to individualcomponents of graphics pipeline 820 or media pipeline 830.

In some embodiments, command streamer 803 directs the operation of avertex fetcher 805 that reads vertex data from memory and executesvertex-processing commands provided by command streamer 803. In someembodiments, vertex fetcher 805 provides vertex data to a vertex shader807, which performs coordinate space transformation and lightingoperations to each vertex. In some embodiments, vertex fetcher 805 andvertex shader 807 execute vertex-processing instructions by dispatchingexecution threads to execution units 852A-852B via a thread dispatcher831.

In some embodiments, execution units 852A-852B are an array of vectorprocessors having an instruction set for performing graphics and mediaoperations. In some embodiments, execution units 852A-852B have anattached L1 cache 851 that is specific for each array or shared betweenthe arrays. The cache can be configured as a data cache, an instructioncache, or a single cache that is partitioned to contain data andinstructions in different partitions.

In some embodiments, graphics pipeline 820 includes tessellationcomponents to perform hardware-accelerated tessellation of 3D objects.In some embodiments, a programmable hull shader 811 configures thetessellation operations. A programmable domain shader 817 providesback-end evaluation of tessellation output. A tessellator 813 operatesat the direction of hull shader 811 and contains special purpose logicto generate a set of detailed geometric objects based on a coarsegeometric model that is provided as input to graphics pipeline 820. Insome embodiments, if tessellation is not used, tessellation components(e.g., hull shader 811, tessellator 813, and domain shader 817) can bebypassed.

In some embodiments, complete geometric objects can be processed by ageometry shader 819 via one or more threads dispatched to executionunits 852A-852B, or can proceed directly to the clipper 829. In someembodiments, the geometry shader operates on entire geometric objects,rather than vertices or patches of vertices as in previous stages of thegraphics pipeline. If the tessellation is disabled the geometry shader819 receives input from the vertex shader 807. In some embodiments,geometry shader 819 is programmable by a geometry shader program toperform geometry tessellation if the tessellation units are disabled.

Before rasterization, a clipper 829 processes vertex data. The clipper829 may be a fixed function clipper or a programmable clipper havingclipping and geometry shader functions. In some embodiments, arasterizer and depth test component 873 in the render output pipeline870 dispatches pixel shaders to convert the geometric objects into theirper pixel representations. In some embodiments, pixel shader logic isincluded in thread execution logic 850. In some embodiments, anapplication can bypass the rasterizer and depth test component 873 andaccess un-rasterized vertex data via a stream out unit 823.

The graphics processor 800 has an interconnect bus, interconnect fabric,or some other interconnect mechanism that allows data and messagepassing amongst the major components of the processor. In someembodiments, execution units 852A-852B and associated cache(s) 851,texture and media sampler 854, and texture/sampler cache 858interconnect via a data port 856 to perform memory access andcommunicate with render output pipeline components of the processor. Insome embodiments, sampler 854, caches 851, 858 and execution units852A-852B each have separate memory access paths.

In some embodiments, render output pipeline 870 contains a rasterizerand depth test component 873 that converts vertex-based objects into anassociated pixel-based representation. In some embodiments, therasterizer logic includes a windower/masker unit to perform fixedfunction triangle and line rasterization. An associated render cache 878and depth cache 879 are also available in some embodiments. A pixeloperations component 877 performs pixel-based operations on the data,though in some instances, pixel operations associated with 2D operations(e.g. bit block image transfers with blending) are performed by the 2Dengine 841, or substituted at display time by the display controller 843using overlay display planes. In some embodiments, a shared L3 cache 875is available to all graphics components, allowing the sharing of datawithout the use of main system memory.

In some embodiments, graphics processor media pipeline 830 includes amedia engine 837 and a video front end 834. In some embodiments, videofront end 834 receives pipeline commands from the command streamer 803.In some embodiments, media pipeline 830 includes a separate commandstreamer. In some embodiments, video front-end 834 processes mediacommands before sending the command to the media engine 837. In someembodiments, media engine 837 includes thread spawning functionality tospawn threads for dispatch to thread execution logic 850 via threaddispatcher 831.

In some embodiments, graphics processor 800 includes a display engine840. In some embodiments, display engine 840 is external to processor800 and couples with the graphics processor via the ring interconnect802, or some other interconnect bus or fabric. In some embodiments,display engine 840 includes a 2D engine 841 and a display controller843. In some embodiments, display engine 840 contains special purposelogic capable of operating independently of the 3D pipeline. In someembodiments, display controller 843 couples with a display device (notshown), which may be a system integrated display device, as in a laptopcomputer, or an external display device attached via a display deviceconnector.

In some embodiments, graphics pipeline 820 and media pipeline 830 areconfigurable to perform operations based on multiple graphics and mediaprogramming interfaces and are not specific to any one applicationprogramming interface (API). In some embodiments, driver software forthe graphics processor translates API calls that are specific to aparticular graphics or media library into commands that can be processedby the graphics processor. In some embodiments, support is provided forthe Open Graphics Library (OpenGL), Open Computing Language (OpenCL),and/or Vulkan graphics and compute API, all from the Khronos Group. Insome embodiments, support may also be provided for the Direct3D libraryfrom the Microsoft Corporation. In some embodiments, a combination ofthese libraries may be supported. Support may also be provided for theOpen Source Computer Vision Library (OpenCV). A future API with acompatible 3D pipeline would also be supported if a mapping can be madefrom the pipeline of the future API to the pipeline of the graphicsprocessor.

Graphics Pipeline Programming

FIG. 9A is a block diagram illustrating a graphics processor commandformat 900 according to some embodiments. FIG. 9B is a block diagramillustrating a graphics processor command sequence 910 according to anembodiment. The solid lined boxes in FIG. 9A illustrate the componentsthat are generally included in a graphics command while the dashed linesinclude components that are optional or that are only included in asub-set of the graphics commands. The exemplary graphics processorcommand format 900 of FIG. 9A includes data fields to identify a targetclient 902 of the command, a command operation code (opcode) 904, andthe relevant data 906 for the command. A sub-opcode 905 and a commandsize 908 are also included in some commands.

In some embodiments, client 902 specifies the client unit of thegraphics device that processes the command data. In some embodiments, agraphics processor command parser examines the client field of eachcommand to condition the further processing of the command and route thecommand data to the appropriate client unit. In some embodiments, thegraphics processor client units include a memory interface unit, arender unit, a 2D unit, a 3D unit, and a media unit. Each client unithas a corresponding processing pipeline that processes the commands.Once the command is received by the client unit, the client unit readsthe opcode 904 and, if present, sub-opcode 905 to determine theoperation to perform. The client unit performs the command usinginformation in data field 906. For some commands an explicit commandsize 908 is expected to specify the size of the command. In someembodiments, the command parser automatically determines the size of atleast some of the commands based on the command opcode. In someembodiments commands are aligned via multiples of a double word.

The flow diagram in FIG. 9B shows an exemplary graphics processorcommand sequence 910. In some embodiments, software or firmware of adata processing system that features an embodiment of a graphicsprocessor uses a version of the command sequence shown to set up,execute, and terminate a set of graphics operations. A sample commandsequence is shown and described for purposes of example only asembodiments are not limited to these specific commands or to thiscommand sequence. Moreover, the commands may be issued as batch ofcommands in a command sequence, such that the graphics processor willprocess the sequence of commands in at least partially concurrence.

In some embodiments, the graphics processor command sequence 910 maybegin with a pipeline flush command 912 to cause any active graphicspipeline to complete the currently pending commands for the pipeline. Insome embodiments, the 3D pipeline 922 and the media pipeline 924 do notoperate concurrently. The pipeline flush is performed to cause theactive graphics pipeline to complete any pending commands. In responseto a pipeline flush, the command parser for the graphics processor willpause command processing until the active drawing engines completepending operations and the relevant read caches are invalidated.Optionally, any data in the render cache that is marked ‘dirty’ can beflushed to memory. In some embodiments, pipeline flush command 912 canbe used for pipeline synchronization or before placing the graphicsprocessor into a low power state.

In some embodiments, a pipeline select command 913 is used when acommand sequence requires the graphics processor to explicitly switchbetween pipelines. In some embodiments, a pipeline select command 913 isrequired only once within an execution context before issuing pipelinecommands unless the context is to issue commands for both pipelines. Insome embodiments, a pipeline flush command 912 is required immediatelybefore a pipeline switch via the pipeline select command 913.

In some embodiments, a pipeline control command 914 configures agraphics pipeline for operation and is used to program the 3D pipeline922 and the media pipeline 924. In some embodiments, pipeline controlcommand 914 configures the pipeline state for the active pipeline. Inone embodiment, the pipeline control command 914 is used for pipelinesynchronization and to clear data from one or more cache memories withinthe active pipeline before processing a batch of commands.

In some embodiments, commands for the return buffer state 916 are usedto configure a set of return buffers for the respective pipelines towrite data. Some pipeline operations require the allocation, selection,or configuration of one or more return buffers into which the operationswrite intermediate data during processing. In some embodiments, thegraphics processor also uses one or more return buffers to store outputdata and to perform cross thread communication. In some embodiments,configuring the return buffer state 916 includes selecting the size andnumber of return buffers to use for a set of pipeline operations.

The remaining commands in the command sequence differ based on theactive pipeline for operations. Based on a pipeline determination 920,the command sequence is tailored to the 3D pipeline 922 beginning withthe 3D pipeline state 930 or the media pipeline 924 beginning at themedia pipeline state 940.

The commands to configure the 3D pipeline state 930 include 3D statesetting commands for vertex buffer state, vertex element state, constantcolor state, depth buffer state, and other state variables that are tobe configured before 3D primitive commands are processed. The values ofthese commands are determined at least in part based on the particular3D API in use. In some embodiments, 3D pipeline state 930 commands arealso able to selectively disable or bypass certain pipeline elements ifthose elements will not be used.

In some embodiments, 3D primitive 932 command is used to submit 3Dprimitives to be processed by the 3D pipeline. Commands and associatedparameters that are passed to the graphics processor via the 3Dprimitive 932 command are forwarded to the vertex fetch function in thegraphics pipeline. The vertex fetch function uses the 3D primitive 932command data to generate vertex data structures. The vertex datastructures are stored in one or more return buffers. In someembodiments, 3D primitive 932 command is used to perform vertexoperations on 3D primitives via vertex shaders. To process vertexshaders, 3D pipeline 922 dispatches shader execution threads to graphicsprocessor execution units.

In some embodiments, 3D pipeline 922 is triggered via an execute 934command or event. In some embodiments, a register write triggers commandexecution. In some embodiments execution is triggered via a ‘go’ or‘kick’ command in the command sequence. In one embodiment, commandexecution is triggered using a pipeline synchronization command to flushthe command sequence through the graphics pipeline. The 3D pipeline willperform geometry processing for the 3D primitives. Once operations arecomplete, the resulting geometric objects are rasterized and the pixelengine colors the resulting pixels. Additional commands to control pixelshading and pixel back end operations may also be included for thoseoperations.

In some embodiments, the graphics processor command sequence 910 followsthe media pipeline 924 path when performing media operations. Ingeneral, the specific use and manner of programming for the mediapipeline 924 depends on the media or compute operations to be performed.Specific media decode operations may be offloaded to the media pipelineduring media decode. In some embodiments, the media pipeline can also bebypassed and media decode can be performed in whole or in part usingresources provided by one or more general purpose processing cores. Inone embodiment, the media pipeline also includes elements forgeneral-purpose graphics processor unit (GPGPU) operations, where thegraphics processor is used to perform SIMD vector operations usingcomputational shader programs that are not explicitly related to therendering of graphics primitives.

In some embodiments, media pipeline 924 is configured in a similarmanner as the 3D pipeline 922. A set of commands to configure the mediapipeline state 940 are dispatched or placed into a command queue beforethe media object commands 942. In some embodiments, commands for themedia pipeline state 940 include data to configure the media pipelineelements that will be used to process the media objects. This includesdata to configure the video decode and video encode logic within themedia pipeline, such as encode or decode format. In some embodiments,commands for the media pipeline state 940 also support the use of one ormore pointers to “indirect” state elements that contain a batch of statesettings.

In some embodiments, media object commands 942 supply pointers to mediaobjects for processing by the media pipeline. The media objects includememory buffers containing video data to be processed. In someembodiments, all media pipeline states must be valid before issuing amedia object command 942. Once the pipeline state is configured andmedia object commands 942 are queued, the media pipeline 924 istriggered via an execute command 944 or an equivalent execute event(e.g., register write). Output from media pipeline 924 may then be postprocessed by operations provided by the 3D pipeline 922 or the mediapipeline 924. In some embodiments, GPGPU operations are configured andexecuted in a similar manner as media operations.

Graphics Software Architecture

FIG. 10 illustrates exemplary graphics software architecture for a dataprocessing system 1000 according to some embodiments. In someembodiments, software architecture includes a 3D graphics application1010, an operating system 1020, and at least one processor 1030. In someembodiments, processor 1030 includes a graphics processor 1032 and oneor more general-purpose processor core(s) 1034. The graphics application1010 and operating system 1020 each execute in the system memory 1050 ofthe data processing system.

In some embodiments, 3D graphics application 1010 contains one or moreshader programs including shader instructions 1012. The shader languageinstructions may be in a high-level shader language, such as the HighLevel Shader Language (HLSL) or the OpenGL Shader Language (GLSL). Theapplication also includes executable instructions 1014 in a machinelanguage suitable for execution by the general-purpose processor core1034. The application also includes graphics objects 1016 defined byvertex data.

In some embodiments, operating system 1020 is a Microsoft® Windows®operating system from the Microsoft Corporation, a proprietary UNIX-likeoperating system, or an open source UNIX-like operating system using avariant of the Linux kernel. The operating system 1020 can support agraphics API 1022 such as the Direct3D API, the OpenGL API, or theVulkan API. When the Direct3D API is in use, the operating system 1020uses a front-end shader compiler 1024 to compile any shader instructions1012 in HLSL into a lower-level shader language. The compilation may bea just-in-time (JIT) compilation or the application can perform shaderpre-compilation. In some embodiments, high-level shaders are compiledinto low-level shaders during the compilation of the 3D graphicsapplication 1010. In some embodiments, the shader instructions 1012 areprovided in an intermediate form, such as a version of the StandardPortable Intermediate Representation (SPIR) used by the Vulkan API.

In some embodiments, user mode graphics driver 1026 contains a back-endshader compiler 1027 to convert the shader instructions 1012 into ahardware specific representation. When the OpenGL API is in use, shaderinstructions 1012 in the GLSL high-level language are passed to a usermode graphics driver 1026 for compilation. In some embodiments, usermode graphics driver 1026 uses operating system kernel mode functions1028 to communicate with a kernel mode graphics driver 1029. In someembodiments, kernel mode graphics driver 1029 communicates with graphicsprocessor 1032 to dispatch commands and instructions.

IP Core Implementations

One or more aspects of at least one embodiment may be implemented byrepresentative code stored on a machine-readable medium which representsand/or defines logic within an integrated circuit such as a processor.For example, the machine-readable medium may include instructions whichrepresent various logic within the processor. When read by a machine,the instructions may cause the machine to fabricate the logic to performthe techniques described herein. Such representations, known as “IPcores,” are reusable units of logic for an integrated circuit that maybe stored on a tangible, machine-readable medium as a hardware modelthat describes the structure of the integrated circuit. The hardwaremodel may be supplied to various customers or manufacturing facilities,which load the hardware model on fabrication machines that manufacturethe integrated circuit. The integrated circuit may be fabricated suchthat the circuit performs operations described in association with anyof the embodiments described herein.

FIG. 11 is a block diagram illustrating an IP core development system1100 that may be used to manufacture an integrated circuit to performoperations according to an embodiment. The IP core development system1100 may be used to generate modular, re-usable designs that can beincorporated into a larger design or used to construct an entireintegrated circuit (e.g., an SOC integrated circuit). A design facility1130 can generate a software simulation 1110 of an IP core design in ahigh level programming language (e.g., C/C++). The software simulation1110 can be used to design, test, and verify the behavior of the IP coreusing a simulation model 1112. The simulation model 1112 may includefunctional, behavioral, and/or timing simulations. A register transferlevel (RTL) design 1115 can then be created or synthesized from thesimulation model 1112. The RTL design 1115 is an abstraction of thebehavior of the integrated circuit that models the flow of digitalsignals between hardware registers, including the associated logicperformed using the modeled digital signals. In addition to an RTLdesign 1115, lower-level designs at the logic level or transistor levelmay also be created, designed, or synthesized. Thus, the particulardetails of the initial design and simulation may vary.

The RTL design 1115 or equivalent may be further synthesized by thedesign facility into a hardware model 1120, which may be in a hardwaredescription language (HDL), or some other representation of physicaldesign data. The HDL may be further simulated or tested to verify the IPcore design. The IP core design can be stored for delivery to a 3rdparty fabrication facility 1165 using non-volatile memory 1140 (e.g.,hard disk, flash memory, or any non-volatile storage medium).Alternatively, the IP core design may be transmitted (e.g., via theInternet) over a wired connection 1150 or wireless connection 1160. Thefabrication facility 1165 may then fabricate an integrated circuit thatis based at least in part on the IP core design. The fabricatedintegrated circuit can be configured to perform operations in accordancewith at least one embodiment described herein.

Exemplary System on a Chip Integrated Circuit

FIGS. 12-14 illustrate exemplary integrated circuits and associatedgraphics processors that may be fabricated using one or more IP cores,according to various embodiments described herein. In addition to whatis illustrated, other logic and circuits may be included, includingadditional graphics processors/cores, peripheral interface controllers,or general purpose processor cores.

FIG. 12 is a block diagram illustrating an exemplary system on a chipintegrated circuit 1200 that may be fabricated using one or more IPcores, according to an embodiment. Exemplary integrated circuit 1200includes one or more application processor(s) 1205 (e.g., CPUs), atleast one graphics processor 1210, and may additionally include an imageprocessor 1215 and/or a video processor 1220, any of which may be amodular IP core from the same or multiple different design facilities.Integrated circuit 1200 includes peripheral or bus logic including a USBcontroller 1225, UART controller 1230, an SPI/SDIO controller 1235, andan I2S/I2C controller 1240. Additionally, the integrated circuit caninclude a display device 1245 coupled to one or more of ahigh-definition multimedia interface (HDMI) controller 1250 and a mobileindustry processor interface (MIPI) display interface 1255. Storage maybe provided by a flash memory subsystem 1260 including flash memory anda flash memory controller. Memory interface may be provided via a memorycontroller 1265 for access to SDRAM or SRAM memory devices. Someintegrated circuits additionally include an embedded security engine1270.

FIG. 13 is a block diagram illustrating an exemplary graphics processor1310 of a system on a chip integrated circuit that may be fabricatedusing one or more IP cores, according to an embodiment. Graphicsprocessor 1310 can be a variant of the graphics processor 1210 of FIG.12. Graphics processor 1310 includes a vertex processor 1305 and one ormore fragment processor(s) 1315A1315N (e.g., 1315A, 13158, 1315C, 1315D,through 1315N−1, and 1315N). Graphics processor 1310 can executedifferent shader programs via separate logic, such that the vertexprocessor 1305 is optimized to execute operations for vertex shaderprograms, while the one or more fragment processor(s) 1315A-1315Nexecute fragment (e.g., pixel) shading operations for fragment or pixelshader programs. The vertex processor 1305 performs the vertexprocessing stage of the 3D graphics pipeline and generates primitivesand vertex data. The fragment processor(s) 1315A-1315N use the primitiveand vertex data generated by the vertex processor 1305 to produce aframebuffer that is displayed on a display device. In one embodiment,the fragment processor(s) 1315A-1315N are optimized to execute fragmentshader programs as provided for in the OpenGL API, which may be used toperform similar operations as a pixel shader program as provided for inthe Direct 3D API.

Graphics processor 1310 additionally includes one or more memorymanagement units (MMUs) 1320A-1320B, cache(s) 1325A-1325B, and circuitinterconnect(s) 1330A-1330B. The one or more MMU(s) 1320A-1320B providefor virtual to physical address mapping for graphics processor 1310,including for the vertex processor 1305 and/or fragment processor(s)1315A-1315N, which may reference vertex or image/texture data stored inmemory, in addition to vertex or image/texture data stored in the one ormore cache(s) 1325A-1325B. In one embodiment the one or more MMU(s)1320A-1320B may be synchronized with other MMUs within the system,including one or more MMUs associated with the one or more applicationprocessor(s) 1205, image processor 1215, and/or video processor 1220 ofFIG. 12, such that each processor 1205-1220 can participate in a sharedor unified virtual memory system. The one or more circuitinterconnect(s) 1330A-1330B enable graphics processor 1310 to interfacewith other IP cores within the SoC, either via an internal bus of theSoC or via a direct connection, according to embodiments.

FIG. 14 is a block diagram illustrating an additional exemplary graphicsprocessor 1410 of a system on a chip integrated circuit that may befabricated using one or more IP cores, according to an embodiment.Graphics processor 1410 can be a variant of the graphics processor 1210of FIG. 12. Graphics processor 1410 includes the one or more MMU(s)1320A-1320B, cache(s) 1325A-1325B, and circuit interconnect(s)1330A-1330B of the integrated circuit 1300 of FIG. 13.

Graphics processor 1410 includes one or more shader core(s) 1415A-1415N(e.g., 1415A, 1415B, 1415C, 1415D, 1415E, 1415F, through 1315N−1, and1315N), which provides for a unified shader core architecture in which asingle core or type or core can execute all types of programmable shadercode, including shader program code to implement vertex shaders,fragment shaders, and/or compute shaders. The exact number of shadercores present can vary among embodiments and implementations.Additionally, graphics processor 1410 includes an inter-core taskmanager 1405, which acts as a thread dispatcher to dispatch executionthreads to one or more shader core(s) 1415A-1415N and a tiling unit 1418to accelerate tiling operations for tile-based rendering, in whichrendering operations for a scene are subdivided in image space, forexample to exploit local spatial coherence within a scene or to optimizeuse of internal caches.

Apparatus and Method for Rendering Adaptive Mesh Refinement Data

As mentioned, one widely used AMR scheme is the Berger-Colella (BC)scheme which is illustrated in FIG. 15. On the left side, 1501, thescheme uses a set of successively finer grids (on a discrete number oflevels), where each child level is a constant refinement factor finerthan the parent. Grids on finer levels may overlap multiple cells and“overwrite” the coarser levels' cell values (as indicated by the shadedcoarser cells in FIG. 15). Finer grids may overlap boundaries of gridson coarser levels, but will always be aligned to cell boundaries; soevery cell on a coarse level is either a final leaf cell, or fullyrefined on a finer level. Data values in BC are specified for the centerof each cell. The right area 1502 illustrates a 2D example of the finalleaf cells with a refinement factor of 2.

The problem with rendering BC AMR data is that the hierarchical andadaptive structure of the data creates challenges for existing renderingtechniques such as volume rendering. In particular, that fact that BCuses cell-centered data means that even though the cells from differentlevels align perfectly, their respective data points at the cellcenters—and thus, the dual grids used for tri-linear interpolation—donot, as illustrated by data points 1601 through 1606 in FIG. 16a . Datapoints 1601, 1602, 1603, and 1604 are all cell centered data points onthe coarse level, and together form a dual cell 1607 which can be usedto tri-linearly interpolate between these data points. The area to theright of 1603 and 1604 would be part of a similar dual cell 1608(spanned by data points 1603 through 1606); however, this dual cell doesnot align with—and instead partly overlaps—the dual cell 1609 on thefiner level side of the level boundary. In particular, in BC-AMR, cellsalign across levels, but their cell centers—and thus, the dual gridsused for interpolation do not. This makes it tricky to create a smoothinterpolant that is easy to evaluate. FIG. 16b illustrates a smoothcontinuous interpolation achieved through “stitching” across boundariesusing tets, but is tricky and costly. That is, in entirely coarseregions one can do a simple trilinear interpolation on the “dual” gridspanned by the cell centers on the coarse grid; in regions that lieentirely within finely represented regions one can do the same on thefine regions, but at the boundaries this is not easily possible.

Note that other types of AMR data—in particular, vertex-centeredschemes—can be more easily rendered using techniques such as the one by[Verdiere et al] (See References below). BC, however, is stillchallenging. There are four well known approaches to rendering AMR data:

Resampling the data to a structured regular grid, and rendering this.This makes rendering trivial, but typically leads to loss of data.Simulations use AMR exactly because representation at the finest levelis infeasible for any but the most trivial examples, so resampling forrendering typically has to rely on subsampled representations.

Nearest-neighbor reconstruction: Rather than interpolating between“neighboring” data points one simply picks the value of the cell thatthe data point lies in. This however creates undesired “artifacts” inparticular for “spiky” transfer functions. Even in coarse regions thereconstructed scalar field does not vary smoothly between neighboringsamples, but “jumps” at cell boundaries.

Grid homogenization and compositing [Kreylos et al], works bypartitioning the domain into non-overlapping regions with samerefinement level, rendering those individually, and compositing themtogether. This does however not ensure smooth interpolation across gridboundaries. In fact, the paper seems to use a cell projection scheme.

Interpolating with tet-stitching as proposed by [Weber et al]. In thiscase neighboring cells from different refinement levels are connectedthrough tetrahedral shapes and/or pyramids, inside of which one performslinear interpolation, as shown in FIG. 16B. The problem with thisapproach is that it requires generation of these tetrahedral shapes(which in itself is not trivial), and then requires finding those duringsampling, which is costly.

I. Overview

One embodiment of the invention includes one or more of the followingfour components:

a) A “multi-octree” data structure or a kd-tree data structure thatgeneralizes the type of data used in BC-AMR, and makes it easier toreason about things like neighbors, parents, children, etc., of a givencell.

b) A set of interpolation schemes based on this data structure

c) A specific interpolation schemes based on this data structure that isboth smooth and continuous, and that relies on repeated trilinearinterpolation

d) A ray tracing-based rendering approach that uses this interpolationscheme to render BC-AMR data.

One embodiment of the invention relies on the following key kernelswhich may be executed, regardless of the type of data structure used(e.g., kd-tree or multi-octree):

-   -   a) Find the “closest existing cell” (as defined below) for a        given 3D position P and level L; and return the parameters that        describe this cell (e.g., its coordinates, level, center, and/or        value);    -   b) Find the closest existing leaf cell for a position P;    -   c) Find the closest existing leaf cell for a given set of        logical cell coordinates (i,j,k,l);    -   d) Given six coordinates x0,x1,y0,y1,z0,z1 and a level L; find        the eight closest existing cells for the 8 points (x0,y0,z0),        (x1,y0,z0), . . . etc, on level L; and    -   e) Given a logical dual cell coordinate (i,j,k;l), find the        eight closest existing cells for that dual cell (ie, cells        (i,j,k;l), (i+1,j,k;l), (i,j+1,k;l), . . . etc).        Depending on the implementation, these operations may be        implemented either in a kd-tree, or with the multi-octree as        described in detail below.

Terminology

The following terminology is used throughout this application:

Logical Nested Grid Space:

In order to abstract from the actual input data layout (individualbricks on different levels) cells are referred to in logical nested gridspace. The AMR data can be viewed as a succession of levels L^((l))(l=0. . . maxLevel), where each level is logically a structured grid ofN_(x) ^((l))×N_(y) ^((l))×N_(z) ^((l)) logical cells C_(i,j,k) ^((l)),with the sole caveat that some of these cells actually exist in a givenBC data set, and some do not. Those logical cells that map to actualinput data points are referred to as actual cells, while those that donot as virtual cells. Each cell C has a center C_(P), a level C_(l),etc; actual cells also have a data value C_(v), while virtual ones donot.

This grid can also be logically extended to infinity by simplyconsidering all cells outside the root level's bounding box as virtual.For any level l and 3D point P an operator C^((l))(P) is defined thatmaps P to the logical cell that P lies in.

Closest Existing Cell:

For each logical cell C a definition is used for the closest existingcell (CEC) Ĉ of C: if C is an actual cell, its CEC is just that; if itis not, Ĉ is defined as the actual leaf cell that C.p lies in. Sincethis makes sense only for cells that lie in the bounding box of theinput data we assume that this CEC-operator will, for any P outside thisbounding box, first move P to its respectively closest position insidethe domain.

Similarly we can define, for any 3D position P, the closest existinglevel-l cell Ĉ^((l))(P) (as the CEC of C^(l)(P)); and the closestexisting leaf (CEL) Ĉ(P).

Dual Cell:

Using logical grid terminology allowed for more straightforwardreasoning about logical cells C_(i,j,k) ^((l)). In a similar fashion,logical dual cells D_(i,j,k) ^((l)) (spanned by C_(i,j,k) ^((l)) andC_(i+l,j+k,k+1) ^((l)) may also be considered. Again as was done forcells, it is assumed that there is a kernel D^((l))(P) that computes thecoordinates of the dual cell, as well as the CEC of each of its 8 cornervertices. For each of these corners its logical coordinates C may beaccessed as well as actual coordinates (and value) of its CEC, Ĉ. Thisallow for determining which of the corners C actually exists (C=Ĉ), andwhich ones are virtual (C≠Ĉ). It is perfectly valid for the dual cell tolie partly or entirely outside the bounding box; and/or for some (oreven all) of the corners to map to exactly the same CEC.

Cell Location:

In all our methods it is assumed that it is possible to efficientlyquery cells, dual cells, etc. In particular, in our pseudo-codes weassume a kernel findLeaf(P) that finds the CEL of P, a findCell(l,P)that finds the CEC C^((l))(P), a findDual(l,P) that finds the level-ldual cell (and the CECs of its corners), and a D.lerp(P) that computestri-linear interpolation inside D. Ways of realizing these kernels willbe discussed below.

II. Cell Based Reconstruction Techniques

Similar to nearest-neighbor filtering for textures or structured data,one way to perform reconstruction is to look up the leaf cell containingthe query point, and return its value:

  float nearest(P)  C = findLeaf(P)  return C.vThis method is fast and simple, but not continuous even in same-levelregions, which very much limits is usefulness.

Single-Level Interpolation

Thanks the logical grid abstraction each specific level can be viewed asa structured grid, with values for non-existing cells defined throughthe CEC operator. In particular, this allows for picking any logicallevel I, and tri-linearly interpolating on it:

  float lerpOnLevel(l,P)  D = findDual(l,P)  return D.lerp(P)This is cheap and continuous, but not adaptive. To make it such, we canpick the level based on the sample's leaf level:

  float leafLevelLerp(P)  C = findLeafCell(p)  return lerpOnLevel(C.l,P)This method is no longer continuous across level boundaries, butotherwise already quite useful: it is adaptive, locally trilinear,simple, and still rather fast. In particular, in all regions exceptboundaries it is the same as tri-linear interpolation on that givenregion's refinement level.

Blending Between Levels

The cause of the previous method's discontinuities is that while eachlevel's interpolant was continuous, the method we used for selecting thelevel was not. One way of fixing this is to smoothly blend betweenlevels. In particular, virtual cells can be viewed as transparent, andactual ones as opaque. Once this is done, opacities of 1 and 0 can beassigned to the centers of actual respectively virtual cells, and we canthen trilinearly interpolate between these. This yields a continuousblending function that can be used to blend between any level l and thecoarser ones below:

  float blendNaive(P)  float f = 0.f;  for (level=0,1,..MAXLEVEL)  (f_l,a_l) = lerpOnLevel(l,P)   if (a_l == 0) break   f =a_l*f_l+(1-_l)*f  return f

In homogeneous regions, this method is the same as tri-linearinterpolating on that level; across boundaries it smoothly blendsbetween the adjoining regions' interpolants. This method is thusadaptive and continuous; and (though less obviously so) interpolating.

Though these are nice properties to have, as just explained this methodwould be expensive, as it would have to perform a dual-cell look-up onevery level. In practice, however, very few levels will contribute toany point {right arrow over (X)}: many fine levels will be completelytransparent at {right arrow over (X)}:, and everything below acompletely opaque level would be weighted by 0. This suggests anoptimization where we either start at the coarsest level and blend“upwards” until we reach a completely transparent level (at which pointno finer levels can contribute); or where we start at the finest one andblend “downwards” until we reach a completely opaque one. Even moreinterestingly, we can start at the leaf level of {right arrow over(X)}:, and then blend both upwards and downwards until the finest andcoarsest contributing levels have been found. This can lead tosignificant performance gains over the naïve blending, and is what wewill be using in our evaluation:

  float blendFast(P)  // find leaf level, and lerp  C = findLeafCell(P) D = findDualCell(C.l,P)  f = D.lerp( )  // blend towards finer  D′ = D for (l = C.l+1 ... MAXLEVEL)   if (all vertices of D′ are leaves) break  D′ = findDualCell(l,P)   (f_l,a_l) = D′.lerp(P)   f = a_l*f_l +(1-a_l)*f  // blend towards coarser  if (any vertices in D are virtual){   a = D.lerpAlpha(P)   f = f*a   for (l = C.l-1 ... 0)    D′ =findDualCell(l,P)    f += (1-a) * D′.lerp(P)    if (all vertices in D′exist) break   a += (1-a)*D′.lerpAlpha(P)  // done  return f;

Reconstruction Via Basis Functions

The blend method is both adaptive and continuous (i.e., crack-free)—butcan lead to an artifact sometimes referred to as ghosting. The root ofthe problem is that in those areas where the blend function blendsacross a level boundary, this blending involves cells whosecontributions are questionable. On the fine level some cells are virtualand filled by closest existing cells; and on the coarse level some cellswill be inner cells whose values should actually be superseded by theirfiner level refinements. Obviously this could be avoided only by methodsthat only use actual leaf values.

Though often seen as a form of “blending” between extremal values,regular tri-linear interpolation can also be viewed as the sum of 8hat-shaped basis functions located at the dual cell's corners:

${{{lerp}\left( {\overset{\rightarrow}{p},D} \right)} = {\sum\limits_{C \in {{corners}{(D)}}}\; {{{\hat{H}}_{C}\left( \overset{\rightarrow}{p} \right)}C_{v}}}},$

using the hat-shaped basis functions

$\; {{{\hat{H}}_{C}\left( \overset{\rightarrow}{p} \right)} = {\max\left( {{1 - \frac{{{\overset{\rightarrow}{C} \cdot p} - \overset{\rightarrow}{p}}}{C \cdot w}},0} \right)}}$

For each cell C this basis function would be centered at C_(P) and havea support width of ±C_(W)⋅, where C_(W) is the width of cell C.

Borrowing some concepts from scattered data interpolation techniques(see, e.g., [FN80]) we may now view our AMR data points as a sort ofscattered data points (C_(i))^(N) _(i=0) with basis functions Ĉ,and—using Franke-style scattered data interpolation—can reconstruct anypoint using a weighted and re-normalized sum of those basis functions:

${{AMR}_{hats}\left( \overset{\rightarrow}{p} \right)} = {\frac{\sum_{c_{i}}{{H_{c_{i}}\left( \overset{\rightarrow}{p} \right)}{c_{i} \cdot v}}}{\sum_{c_{i}}{H_{c_{i}}\left( \overset{\rightarrow}{p} \right)}}.}$

Though Franke's scattered-data interpolation method does not specifywhich basis functions to use (and is often used with Gaussian or otherbasis function), our choice of Ĥ_(c) is deliberate: they are easy tocompute, and in most regions will automatically yield exactly the sameinterpolant as tri-linear interpolation. Around boundaries thesuperposition of basis functions results from different levels, whichwill smoothly blend between levels; and as virtual or inner cells arenot used ghosting is significantly reduced.

For any point P, computing this interpolant requires finding all leafcells C that have non-zero contribution at P. For our choice of basisfunction, on each level L only the eight corners of P's dual cell canpossibly contribute, leading to a very simple implementation:

  float AMR_hats(P) =  float sum_weights = 0  float sum_weightedValues =0  for (l = 0 ...)   D=findDualCell(P)   foreach corner cell C of D   if (C is a leaf cell)     sum_weights += H_hat(P,C)    sum_weightedValues += H_hat(P,C)*C.v   if (none of the C in D areinner nodes)    break return sum_weightedValues / sum_weights

On the upside, this interpolant is easy to implement, smooth,continuous, and produces good image quality. On the downside, it is nolonger interpolating, and also it is no longer obvious how to doimplicit ray-isosurface intersection. In terms of performance, thefinest level that contributes can be determined, but a good way ofknowing the coarsest one that does is not known; this means that indeeply refined regions many dual-cell look-ups have to potentially beperformed, which is costly.

Exemplary Architectures

FIGS. 17A and 17B illustrate an exemplary graphics processing engine1700 on which embodiments of the invention may be implemented. Inparticular, in FIG. 17A, a sample-based direct volume renderer 1702includes adaptive mesh refinement (AMR) with multi-octree processinglogic 1710 for performing the AMR techniques described herein usinginput geometry 1701. FIG. 17B illustrates another embodiment whichincludes adaptive mesh refinement with KD-processing logic 1750. Adescription of the embodiment in FIG. 17A which uses a multi-octree datastructure is provided in Section II and a description of the embodimentin FIG. 17B is provided in Section III.

III. Octant Based Reconstruction Techniques

One embodiment of the invention takes advantage of the fact that everycell can be viewed as consisting of 8 octants (i.e., 4 quadrants in 2D),and that when doing so, every quadrant is always on exactly one level,and never overlaps any level boundaries, nor other cells' octants. Forexample, as shown in FIG. 16b , every quadrant of any cell is eithercompletely green, blue, or red; never both. In addition, in oneembodiment, the “new” data points at the corners of these quadrants areused in a way to create an interpolant that is both smooth andcontinuous (see below).

One embodiment of the invention does not consider either cells or dualcells of the original grids, but instead looks at the octants of theinput cells. The problem with interpolation across level boundaries isthat cells align, but cell centers—and thus, dual cells, do not.Octants, however, lie at the intersection of cells and dual cells, asillustrated in FIG. 18A, and do align at level boundaries. At theselevel boundaries the frequency of octants on the fine and coarse sidesof this boundary varies, but coarse ones align to fine ones.Furthermore, the vertices of these (implicit) octants at cell boundariesare free to be chosen, allowing the construction of an interpolant in away that is continuous at the cell boundaries (even those from differentlevels), while still interpolating the original data points (that alwayslie within the cells).

Using this observation, one embodiment of the AMR with multi-octreeprocessing logic 1710 and/or AMR with KD tree processing logic 1750identifies octants, trilinearly interpolates inside these octants, andproperly chooses the interpolation values at the corners of theseoctants (C,Vx,Vy, etc, in FIG. 18B) to create the proper interpolant.These values can be properly chosen, and can be computed efficiently vialinear, bilinear, or trilinear interpolation from neighboring cellvalues.

Smooth Interpolation of BC-AMR Using Repeated Linear Interpolation

In one embodiment of the invention, the interpolation scheme for a pointP=(Px,Py,Pz) proceeds as follows (consult FIGS. 18A-B for the namingscheme used):

1) Find the leaf cell L=(Li,Lj,Lj)(Lm) for P as described above

2) Determine the octant of L that P lies in. This defines 7 new(virtual) data points Vx,Vy,Vz, etc, that coincide with the leaf'sboundaries (see FIGS. 18A-B).

3) Compute the index of (logical) face neighbor Cx in the x direction,and locate the closest node for that index. If that cell existed on L'slevel, determine Vx through interpolation: Vx=avg(V,Cx), where avg(X,Y)refers to the average of the values stored at cells X and Y. If thisnode did not exist on this level (i.e., Cx.l<L.l), compute Vxrecursively through interpolation on level Cx.l. Do the same for Cy/Vy,and Cz,Vz.

4) For edge vertex Vxy, compute and locate neighbors Cx,Cy,and Cyx. Ifall those exist on current levels, let Vxy=avg(V,Cx,Cy,Cxy); otherwiserecursively interpolate Vx on level min(Cx.l,Cy.l,Cxy.l). Do the samefor Vyz and Vxz.

5) For corner vertex Vxyz, compute and locate all 7 neighbors. If allexist on level C.l, let Vxyz=avg(V,Cx, . . . ); else recursivelyinterpolate Vx on level min(Cx.l, . . . ).

6) Tri-linearly interpolate P on octant (V,Vx,Vy, . . . ), and returnthe value.

In this algorithm, “recursively evaluate V on level L” refers toexecuting exactly that same algorithm with the only modification thatthe cell location used in step 1 does not find the leaf cell on thefinest level, but the cell on level L that contains V (and that, ofcourse, it operates on the position of the specified V, not on P). Thescheme can be shown to terminate, and to be continuous and smooth, butthis exceeds this IDF.

Rendering

This interpolation scheme may be used in any sample-based direct volumerenderer such as the sample-based direct volume renderer 1702illustrated in FIGS. 17A-B. The scheme is fully compatible with othertechniques like pre-integration, application of transfer functions,computation of finite difference gradients, etc.

In addition, in one embodiment, these techniques are used for computingimplicit iso-surfaces. To do so a ray may be traced through the set ofall cell octants, and intersected with the tri-linear interpolantdefined by the respective octants' vertex Values C,Vx,Vy, . . . etc.

Variants of the Octant Method

In one embodiment the octant method is modified as follows: First, wefind the octant O as described above. Second, we determine itscorresponding dual cell D and find the 8 CECs for this dual cell'svertices Cx, Cy, . . . Cxy, etc. For each of the octant vertices Vx, Vy,. . . Vxy, . . . etc we then proceed as follows:

-   -   a) For the side neighbor Vx: If the respective neighbor Cx of Vx        exists and is a leaf cell, then Vx does not lie on a boundary,        and is set to the average of C and Vx (same as above). If Cx is        a inner cell, then Vx lies on boundary (with C on the finer side        and Cx on the coarser). In this case we compute the value of Vx        by recursively using this octant method in Cx, for position Vx.        If neither of these cases applies Vx must be on the coarser side        of a boundary, in which case we use a method ‘coarseFill(Vx)’ as        described below. For the other side neighbors Vy and Vz we        perform accordingly.    -   b) For the octant edge vertex Vxy we look at all the neighbor        cells that touch Vxy, which are Cx,Cy, and Cxy. If all of those        cells are leaf cells on the current level we are not at a        boundary, and set Vxy to the average of C,Cx,Cy,and Cxy (same as        above). If either of these three neighbor cells is a inner cell        then Vxy lies on at least one boundary. In this case we find the        coarsest of these three cells, and recursively perform the        octant method for Vxy in this coarsest neighbor. If neither of        these two cases applied we must be on the coarser side of at        least one level boundary. In this case, we set the value of Vxy        using the ‘coarseFill’ method as described below. For the other        edge neighbors Vyz and Vxz we perform accordingly.    -   c) For the corner vertex Vxyz we perform similarly to ‘b’,        except that we consider all neighbor cells Cx, Cy, . . . Cyx, .        . . Cyz. Again we use averaging if we're not on a boundary, use        recursive execution in the coarsest neighbor if at least one        neighbor is a inner node, and use ‘coarseFill’ if neither of        these two cases applied.        In one instantiation we implement ‘coarseFill(P)’ using the Hats        method as described above. In another instantiation we implement        it using the average or weighted average of all leaf cells C        that touch P (using, for example, weights based on each C's        level). In yet another instantiation we compute coarseFill using        the octant method on the coarsest cell touching P. Finally, in        one instantiation we compute coarseFill by the average of C and        the given neighbors (Cx for Vx; Cx,Cy, and Cxy for Vxy, etc)        irrespective of which level they are on.

III. Data Structures and Algorithms to Efficiently Store and Query Cellsand Dual Cells

As illustrated in FIG. 17A, one embodiment of the AMR with multi-octreeprocessing logic 1710 includes a “multi-octree” data structure generator1712 that transforms BC-AMR data 1711 into a multi-octree datastructure. Similarly, as shown in FIG. 17B, one embodiment of the AMRwith KD-tree processing logic 1750 includes a KD-tree data structuregenerator 1752 that transforms the BC-AMR data 1711 into a KD-tree datastructure. As discussed below, both embodiments simplify reasoningrelated to neighbors, parents, children, etc., of a given cell (asdescribed herein). An interpolation module 1713 then implements aspecific interpolation scheme based on this data structure that is bothsmooth and continuous and that relies on repeated trilinearinterpolation. A ray tracing-based rendering module 1713 then uses thisinterpolation scheme to render BC-AMR data.

1. Multi-Octree Data Structures

As the embodiments of the invention rely on repeatedly interpolatingvalues from neighboring cells, a technique of reasoning about“neighbors” of cells is needed (even across multiple levels), as well asa fast and efficient way of finding a cell from a sample point, to findthe neighbors of a given cell.

We first define a logical space of infinitely nested, progressivelyrefined grids. At the root of this space lies a grid G(0) of Nx*Ny*Nzlogical size 1. If each such cell was split into 2×2×2 cells we wouldend up with a grid G(1) of 2Nx*2Ny*2Nz cells of size 0.5. Similarly, atlevel n we would have grid G(n) of 2^(n)Nx*2^(n)Ny*2^(n)Nz of side2^(−n). We enumerate the cells of this infinite scoping of grids as(l,j,k)(m), where m is the grid level, and (l,j,k) is the index in G(m).Using this we can easily argue about neighbors, parent, and children:Each node (ijk)(m) has the 8 children (2i+{0,1},2j+{0,1},2k+{0,1}(m+1},the parent (i/2,j/2,k/2)(m−1), and obvious neighbors.

While this space is easy to reason with, an infinite number of cellsdoes not lend well to a concrete implementation. However, rather thanseeing G(1) as a grid of 2Nx*2Ny*2Nz cells these same cells can bearranged in Nx*Ny*Nz blocks of 2×2×2 cells that all have a common parent(same for other levels). As such, the same data structure can be encodedas a grid of Nx*Ny*Nz root nodes that each point to their 2×2×2children—or use a NULL pointer to indicate a leaf. In addition, eachnode can also store a data value. Obviously, any cell in thismulti-octree maps to an index (l,j,k)(m) in the virtual nested gridspace (though not vice versa). Similarly, the “closest existing leafcell” can be uniquely defined for any arbitrary index (ijk)(m) (even forthose that do not actually exist) as the deepest actually existent leafnode that would have been a predecessor of this virtual node.

Multi-Octree Representation of BC-AMR

Due to the properties of BC—in particular, that any grid cell on anylevel is either not covered at all by another grid on a deeper level, orfully covered by it—each BC AMR input is transformed with power-of-tworefinement factors into the Multi-Octree data structure. In oneembodiment, the values Nx*Ny*Nz are chosen as the dimensions of theBC-AMR root grid. Then, assuming a refinement factor of 2 each inputgrid may be mapped on level m into a range of cell coordinates.

All such nodes can be created in the multi-octree data structure, andfilled with the respective input values. For refinement factors of 4 newrefinement levels of 2 can be inserted and filled with down-filteredversions of the actual “factor-4” grids. This creates new factor-2 gridsthat didn't exist in the input, but since all of their cells areeventually overwritten by the factor-4 cells this is not a problem otherthan a (slight) increase in memory consumption.

Multi-Octree algorithms are readily defined for:

Finding the root node's coordinates (i0,j0,k0) for any giving index(ijk)(m) as (i0,j0,k0)=(i>>m,j>>m,k>>0).

Finding the root node's coordinates for a given 3D position P=(x,y,z) byprojecting it into the logical grid and computing the integercoordinates of this cell.

Finding the closest existing node for a given index (ijk)(m) by startingat (ijk)(m)'s root node and following its corresponding octree untileither level m is reached, or a leaf node is reached. A pointer isreported to that node and the actual found index. In one instantiation,in any given level m we select the octree's respective child node bylooking at the m'th bits of indices i, j, and k.

Finding the level of any given node by returning its level index, m.

Finding the leaf cell (ijk)(m) for any point P=(x,y,z) by projecting itinto the root grid, finding the root node for P, and walking itscorresponding octree until a leaf is found.

Finding the respective CEL each for a number of different points P0,P1,. . . Pn (for example, the 8 vertices of a dual cell D). In oneinstantiation we achieve this using the steps:

-   -   a) create a list of query points yet to be processed, and        initialize it to P0,P1, . . . Pn.    -   b) Take one point P from this list, and find the CEL L for P as        described above.    -   c) Find all points P′ in the list that map to the given leaf        cell L, and return L as answer for those P's queries. Remove all        such P′ from the list    -   d) Iterate to b′ until the list is empty.    -   In one instantiation, we perform this operation using vector        instructions to process multiple P's in parallel.

FIGS. 18A-B illustrate an exemplary geometry for a cell, one of itsoctants, the vertices thereof, and neighbor cells. In FIG. 18A, for eachleaf cell C, any point P can be assigned one of the 8 octants defined bythe cell's center point, C. That octant (in 3D) has 3 face neighborsVx,Vy,Vz, 3 edge neighbors Vxy,Vxz,Vyz, and 1 corner neighbor Vxyz.Specifying scalar values for these points allows trilinear interpolationinside this octant. In FIG. 18B, for each octant, each cell has 7“logical” neighbor cells on the level of C, named Cx,Cy, etc (thoughthey may not actually exist, they will have a parent that does). Thegiven octant lies at the intersection of the cell and that dual cellspanned by the neighbors, allowing the values at V to be defined in away that satisfies the desired interpolation criteria.

Possible Extensions

A variety of extensions may be implemented. For example, thesetechniques may be used to render octree data (e.g., sparse voxeloctrees). Any structured volume can be represented in the form ofmulti-octree, using either lossy or lossless compression. This means thetechnique can be used to render octree-compressed voxel data. Thesetechniques are also applicable to higher order interpolants, such asWavelet-compressed volume data. For high sample rates, one can use acache for already-evaluated octants. The costly recursive evaluationonly happens at level boundaries. It should be possible to precomputeand store all octant vertices at those cell boundaries. The nature ofthe data structure naturally lends to adaptive sample schemes where thedensity of volume samples is chosen relative to the cell size at thispoint.

Refinement factors other than 2 may also be used, as long as each leafcell is logically subdivided into R×R×R sub-cells (R being therefinement factor). The math and actual algorithm are more convolved,but the same concept applies. The data structure naturally lends to ascheme where inner nodes store more information on their children'svalues (such as value ranges, value distributions, variance,approximations, etc). These can then be used, for example, forhierarchical culling (iso-surfaces), for space skipping (DVR),adaptively choosing sample rates, etc.

The same scheme can also be used for crack-free iso-surface extractionby operating a “Marching Cubes” variant on the octants of all cells.Other than for visualization, these techniques are useful for renderingother compressed volumetric data (e.g., volumetric effects in movierendering). Ultimately, these techniques provide a smooth interpolationscheme for general (multi-)octree-like data that can, in principle, gobeyond graphics applications (for example, in the simulation codesthemselves). These techniques may also be used on non-rectilinear grids.

2. KD-Tree AMR Data Structures

Irrespective or the ray tracing in which the kernels described hereinwill be used, efficient techniques are needed to compute the celllocation kernels they are all built on.

Inspired by the regularity of the implicit grid space, the embodimentillustrated in FIG. 17A and described above in Section 1 used amulti-octree data structure in which an octree with a branching factorof R³ in each node was built for each cell of the root level. The celllocation in this octree was simple; and with a branching factor of R³the memory overhead for inner nodes was relatively low. However, thisdata structure requires the input data to be reformatted, meaning itwill not directly operate on native VTK data, and requires at least onecopy of such data.

To avoid this, an alternative embodiment is illustrated in FIG. 17Bwhich includes adaptive mesh refinement with KD-tree processing logic1750 to perform the operations described below (referred to as“AMR-KDTree”). In this embodiment, the entirety of all bricks (acrossall levels) are evaluated, and the world space bounding box of thesebricks is computed. This space is then recursively partitioned asfollows. First, a list of all block boundaries that intersect the spaceto be partitioned is determined (each such boundary defines anaxis-aligned plane). One of those is then picked as a kd-treepartitioning plane such as the one closest to the spatial median. Thispartitioning plane is then used to partition the current domain intoleft and right halves.

All blocks in the current region are evaluated and sorted by the AMRwith KD-tree processing logic 1750 into those overlapping the left half,and those overlapping the right; those that overlap both (which ispossible in B/C AMR) go into both. Finally, left and right halves arerecursively processed until no more boundary plane overlaps the currentregion, in which case, a leaf is generated.

By design, each leaf will contain exactly one brick for each levelcovered by that leaf's region. These bricks are sorted by descendinglevel, so the first entry is always the finest (i.e., leaf) level, etc.This data structure is very light-weight, and can be built over whateverexternal memory is used for storing the bricks' voxels. In particular,this data structure can be built over an existingvtkHierarchicalBoxDataSet structure as used by ParaView's and Visit'sChombo readers, without replicating any of the voxels. An obviousalternative is to store bricks by ascending level, with all operationsmodified accordingly.

The previously mentioned cell location kernels—findLeaf, findCell,etc—are easy to implement on top of this data structure. A kd-tree pointlocation may be performed by the AMR with KD-tree processing logic 1750for the sample point P until a leaf is reached. In that leaf, the brickB is picked for the desired level, and the resulting voxel lookupperformed in this brick's structured voxel grid.

For dual cell lookups, all or at least some of the 8 corner lookups willend up in the same brick quite commonly. This may be exploited in aspecial kernel that looks up all 8 corners in one traversal similar tothe one described for the multi-octree. In one instantiation we achievethis using the steps:

-   -   e) create a list of query points yet to be processed, and        initialize it to P0, P1, . . . Pn.    -   f) Take one point P from this list, and find the CEL L for P as        described above.    -   g) Find all points P′ in the list that map to the given leaf        cell L, and return L as answer for those P's queries. Remove all        such P′ from the list    -   h) Iterate to ‘b’ until the list is empty.        In one instantiation, we perform this operation using vector        instructions to process multiple P's in parallel. In one        instantiation we perform this operation for the 8 corners of a        dual cell; in another we perform it for an arbiraty number of        query points as provided by the application.

IV. Integration with an Exemplary Ray Tracing Framework

Though the reconstruction methods and kernels are generally applicable,for the remainder of this paper we consider an implementation within aparticular ray tracing framework, referred to as OSPRay [WJA*16]. OSPRayalready provides a ray tracer, a renderer that supports volume raycasting, and with ready abstractions to implement new volume types. Tomake it support the techniques described herein, the data structureswere set up and the kd-tree built; the cell location kernels executed,and the reconstructions performed as described above.

Since OSPRay makes use of ISPC [PM12] for all performance-critical codethe cell location and reconstruction kernels were implemented in ISPC;all boilerplate and data structure construction code is written inscalar C++, with data structures shared by both sides. Once therespective ospray::ChomboVolume data type was added, it worked out ofthe box with OSPRay's renderers.

High-Performance Cell and Dual-Cell Query

For all of the reconstruction kernels described above, the key factoraffecting the final rendering performance is how quickly cell and dualcell queries are performed. While the AMR KD-tree processed by the AMRwith KD-tree processing logic 1750 provides the right algorithmicinfrastructure, a high-performance implementation is criticallyimportant. Initially, as a proof of concept, intentionally simple,highly flexible, and purely scalar C++ kernels were used for celllocation, and dual-cell queries were implemented via 8 separate cellqueries. These kernels worked well, but turned out to be exceedinglycostly.

Optimized ISPC Cell Query

To improve on this, these kernels were realized on the ISPC side, alwaysperforming N reconstructions (and correspondingly, N cell/-dual cellqueries) in parallel (where N is the vector width of the underlying CPUarchitecture). In addition to such vectorizing these kernels, thesekernels were optimized where possible. For example, in one embodiment,rather than operating on logical integer IDs for cells and levels, cellsare referenced by their (float) center point and levels by their (float)center width, which not only better utilizes the floating pointcomputations, but also minimizes register pressure and stack space,avoids many costly int-to-float conversions when traversing the datastructure, and often allows for utilizing modern vector units'multiply-add capabilities (e.g., even some of the address computationsinside each brick can be done in floating point).

In addition, to minimize data divergence (and consequently, lots ofcostly gathering operations) the cell location was implemented in a“packet” paradigm [WSBW01] in which all N queries stay together whilegoing down the tree; and of course transformed the recursion into amanually maintained stack that gets pushed/popped only when absolutelynecessary. These techniques have demonstrated more than an order ofmagnitude of performance improvement relative to the scalar referencekernels.

Faster Dual-Cell Queries

For the dual-cell query, one embodiment of the AMR with KD-treeprocessing logic 1750 implements a special variant that is built on thepacketized cell location kernel but actually performs all 8 cornerqueries in a single sweep. To do this, the 8 vertex locations are viewedas the intersection of three sets of parallel planes (the planes thatform the boundary of the dual cell) and traversed down the kd-tree. Ateach kd-tree node, the side of the kd-tree plane the respective queryplanes lie is determined, and consequently the planes active in a givensubtree are tracked with only 6 state variables (of course, onlysubtrees with at least one active plane in each pair of planes need tobe traversed). Once a leaf is reached, the 6 active planes defines whichof the 8 corner values are active, and all those can be filled from thatleaf.

REFERENCES

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In embodiments, the term “engine” or “module” or “logic” may refer to,be part of, or include an application specific integrated circuit(ASIC), an electronic circuit, a processor (shared, dedicated, orgroup), and/or memory (shared, dedicated, or group) that execute one ormore software or firmware programs, a combinational logic circuit,and/or other suitable components that provide the describedfunctionality. In embodiments, an engine or a module may be implementedin firmware, hardware, software, or any combination of firmware,hardware, and software.

Embodiments of the invention may include various steps, which have beendescribed above. The steps may be embodied in machine-executableinstructions which may be used to cause a general-purpose orspecial-purpose processor to perform the steps. Alternatively, thesesteps may be performed by specific hardware components that containhardwired logic for performing the steps, or by any combination ofprogrammed computer components and custom hardware components.

As described herein, instructions may refer to specific configurationsof hardware such as application specific integrated circuits (ASICs)configured to perform certain operations or having a predeterminedfunctionality or software instructions stored in memory embodied in anon-transitory computer readable medium. Thus, the techniques shown inthe figures can be implemented using code and data stored and executedon one or more electronic devices (e.g., an end station, a networkelement, etc.). Such electronic devices store and communicate(internally and/or with other electronic devices over a network) codeand data using computer machine-readable media, such as non-transitorycomputer machine-readable storage media (e.g., magnetic disks; opticaldisks; random access memory; read only memory; flash memory devices;phase-change memory) and transitory computer machine-readablecommunication media (e.g., electrical, optical, acoustical or other formof propagated signals—such as carrier waves, infrared signals, digitalsignals, etc.).

In addition, such electronic devices typically include a set of one ormore processors coupled to one or more other components, such as one ormore storage devices (non-transitory machine-readable storage media),user input/output devices (e.g., a keyboard, a touchscreen, and/or adisplay), and network connections. The coupling of the set of processorsand other components is typically through one or more busses and bridges(also termed as bus controllers). The storage device and signalscarrying the network traffic respectively represent one or moremachine-readable storage media and machine-readable communication media.Thus, the storage device of a given electronic device typically storescode and/or data for execution on the set of one or more processors ofthat electronic device. Of course, one or more parts of an embodiment ofthe invention may be implemented using different combinations ofsoftware, firmware, and/or hardware. Throughout this detaileddescription, for the purposes of explanation, numerous specific detailswere set forth in order to provide a thorough understanding of thepresent invention. It will be apparent, however, to one skilled in theart that the invention may be practiced without some of these specificdetails. In certain instances, well known structures and functions werenot described in elaborate detail in order to avoid obscuring thesubject matter of the present invention. Accordingly, the scope andspirit of the invention should be judged in terms of the claims whichfollow.

What is claimed is:
 1. A graphics processing apparatus comprising: atree data structure generator to transform adaptive mesh refinement(AMR) data into a multi-octree or AMR kd-tree data structure,respectively; an interpolator to implement an interpolation scheme basedon the multi-octree or kd-tree data structure to generate interpolatedresults, the interpolation scheme using repeated linear interpolation;and a ray tracing-based renderer to use the interpolated results torender image frames using ray tracing techniques.
 2. The graphicsprocessing apparatus as in claim 1 wherein the multi-octree or kd-treedata structure is to generalize types of data used in an AMR datastructure.
 3. The graphics processing apparatus as in claim 1 whereinthe AMR data comprises BC (Berger and Colella)-AMR data.
 4. The graphicsprocessing apparatus as in claim 1 wherein the AMR data comprises aplurality of cells at a plurality of different levels.
 5. The graphicsprocessing apparatus as in claim 4 wherein the plurality of cells arelogically subdivided into octants to generate the multi-octree datastructure.
 6. The graphics processing apparatus as in claim 5 whereinthe interpolator is to perform trilinear interpolation inside theoctants and to choose interpolation values at corners of the octants togenerate the interpolated results.
 7. The graphics processing apparatusas in claim 6 wherein, for a given point P, the interpolator performsthe operations of: find a leaf cell L=(Li,Lj,Lj)(Lm) for P; determinethe octant of L that P lies in, defining seven new data points; computean index of a logical face neighbor in the x direction, and locate theclosest node for that index; for an edge vertex, compute and locateneighbors; for a corner vertex, compute and locate all seven neighbors;and tri-linearly interpolate P on the octant, and return the value. 8.The graphics processing apparatus as in claim 1 wherein the tree datastructure generator is to transform each AMR data input withpower-of-two refinement factors into the multi-octree data or kd-treedata structure.
 9. A method comprising: transforming adaptive meshrefinement (AMR) data into a multi-octree data structure or kd-tree datastructure; implementing an interpolation scheme based on themulti-octree or kd-tree data structure to generate interpolated results,the interpolation scheme using repeated linear interpolation; andperforming ray tracing to render image frames using the interpolatedresults.
 10. The method as in claim 9 wherein the multi-octree orkd-tree data structure is to generalize types of data used in an AMRdata structure.
 11. The method as in claim 9 wherein the AMR datacomprises BC (Berger and Colella)-AMR data.
 12. The method as in claim 9wherein the AMR data comprises a plurality of cells at a plurality ofdifferent levels.
 13. The method as in claim 12 wherein the plurality ofcells are logically subdivided into octants to generate the multi-octreedata structure.
 14. The method as in claim 13 wherein implementing theinterpolation scheme comprises performing trilinear interpolation insidethe octants and choosing interpolation values at corners of the octantsto generate the interpolated results.
 15. The method as in claim 14wherein, for a given point P, the method further comprising: finding aleaf cell L=(Li,Lj,Lj)(Lm) for P; determining the octant of L that Plies in, defining seven new data points; computing an index of a logicalface neighbor in the x direction, and locate the closest node for thatindex; for an edge vertex, computing and locating neighbors; for acorner vertex, computing and locating all seven neighbors; andtri-linearly interpolating P on the octant, and returning the value. 16.The method as in claim 9 wherein transforming further comprises:transforming each AMR data input with power-of-two refinement factorsinto the multi-octree or kd-tree data structure.
 17. An apparatuscomprising: means for transforming adaptive mesh refinement (AMR) datainto a multi-octree or kd-tree data structure; means for implementing aninterpolation scheme based on this multi-octree data structure togenerate interpolated results, the interpolation scheme using repeatedlinear interpolation; and means for performing ray tracing to renderimage frames using the interpolated results.
 18. The apparatus as inclaim 17 wherein the multi-octree data structure or the kd-tree datastructure is to generalize types of data used in an AMR data structure.19. The apparatus as in claim 17 wherein the AMR data comprises BC(Berger and Colella)-AMR data.
 20. The apparatus as in claim 17 whereinthe AMR data comprises a plurality of cells at a plurality of differentlevels.
 21. The apparatus as in claim 20 wherein the plurality of cellsare logically subdivided into octants to generate the multi-octree datastructure.
 22. The apparatus as in claim 21 wherein implementing theinterpolation scheme comprises performing trilinear interpolation insidethe octants and choosing interpolation values at corners of the octantsto generate the interpolated results.
 23. The apparatus as in claim 22wherein, for a given point P, the means for implementing theinterpolation scheme performs the operations of: finding a leaf cellL=(Li,Lj,Lj)(Lm) for P; determining the octant of L that P lies in,defining seven new data points; computing an index of a logical faceneighbor in the x direction, and locate the closest node for that index;for an edge vertex, computing and locating neighbors; for a cornervertex, computing and locating all seven neighbors; and tri-linearlyinterpolating P on the octant, and returning the value.
 24. Theapparatus as in claim 17 wherein the means for transforming transformseach AMR data input with power-of-two refinement factors into themulti-octree data structure or kd-tree data structure.